Can I not use the default email app with iphone 5s and use gmail, and yahoo mail apps

Instead? Or do I have to keey my gmail account on there because I sync all my contacts from there? Can I use Icloud instead to keep all my contacts and Calendar stuff and not even use the default IO 7 email app and use the Gmail/Yahoo apps instead? I get push emails with the gmail app which is nice to begin with due to the default app does not support gmail push from what I understand. Thanks...

If you just want to use Google Calender then go into settings -> Mail/contacts/calenders and turn off everything but calender for Gmail. You can do the same for iCloud and only sync contacts. You can do this with any account.

If the contacts for your iCloud, Gmail and Yahoo accounts are the same then yes, you can simply use one list for all. That is what I do. I use my iCloud contacts for all of my configured email accounts. Keep in mind, however, that I use the native email app exclusively.